the doctor doesn’t really keep a “room” in the sense that humans do. having a separate space primarily for sleeping doesn’t make much sense for someone who only requires a few hours of sleep at a time, excepting when she’s mid-regeneration cycle. she has very little use for a bed, so she doesn’t keep a bedroom, but she does have a room on the tardis where she prefers to spend the majority of her downtime (assuming she has any): the library.
it’s a massive space filled with millions of books on multiple levels. the doctor has spent so many years amassing this collection of facts and novels and history and poetry. she has them arranged by a system no one else in the universe could possibly understand, and a fair few of them are sitting around on the floor in stacks, still waiting to be properly shelved.
the tardis could easily do this for her, but the doctor requires near-constant stimulation and it helps to always have something there to organize when she gets desperate for a way to keep herself occupied. she can get dangerously restless otherwise.
there’s a desk on almost every level of the doctor’s library, and every last one of them is a mess of books and scattered papers. crumpled pages of thoughts or calculations made during lonely years when she felt it was her burden to protect the universe alone because people are too often lost and killed while traveling with her. there are also an unreasonable number of journals half-filled with notes written in a hundred different languages (she has her favorites on every planet).
when she does rest, it’s on a sofa lofted a few feet off the ground floor. the doctor calls it her office, and it’s where she keeps her favorite books and the desk with her most important (but no less messy) journals and papers.
sometimes, when things are especially quiet on the tardis, and the doctor hasn’t been seen on the bridge in a few hours, she can be found in her office. she’ll be sprawled out on the sofa, a book still open on her chest, and she’s asleep but her eyes never stop darting back and forth beneath her lashes. you see peace, for the doctor, is a relative thing. it’s a mind that never stops racing and feet forever on the run.